12 votes
Accepted

What happens when N increases in N-point DFT

The length N of the DFT is the number of frequency points that will result in the DFT output. Zero padding will result in more frequency samples, however this does not increase frequency resolution, ...
  • 38.3k
7 votes

How does zero-padding affect the magnitude of the DFT?

All effects you see have to do with windowing. Your signal can be seen as a truncated (i.e., rectangularly windowed) sinusoid. If $s[n]$ is your signal, and $w[n]$ is the window, the signal you ...
  • 80.9k
6 votes

Why Zero Padding in the Center of the DFT Interpolates / Upsamples the Signal (Sinc Interpolation / DFT Interpolation / Periodic Interpolation)

What you are experiencing is technically called interpolation by DFT; i.e., interpolating a time-domain sequence $x[n]$ by properly zero filling the middle portion of it's DFT $X[k]$ (and taking the ...
  • 27.1k
5 votes

Advantages/disadvantage of zero padding

Advantages of zero padding: If length of your sequence doesn't correspond to the size that can be handled efficiently with FFT routine (usually powers of prime numbers) then you might want to add ...
  • 10.7k
5 votes
Accepted

How Exactly Does MATLAB Zero Pad Signal?

Lets say you have a vector $ x = {\left[ 1, 2, 3, 4 \right]}^{T} $. You want to have a look on its DFT transform then you apply DFT on it and have the 4 points DFT transform of the data. In MATLAB it ...
  • 42.4k
5 votes
Accepted

Zero padding - High amplitude

I'd like to apply zero padding to it, for better frequency bin resolution. First of all, let's state it one more time that zero padding does not improve frequency resolution of DFT. It'll only ...
  • 27.1k
5 votes

How to Zero Pad in Order to Perform Filtering in the Fourier (Frequency) Domain?

There are 2 things to take under consideration in order to apply 2D Convolution in Frequency Domain: Padding and Shifting the Filter in order to match the size of the image. See my answer to Applying ...
  • 42.4k
4 votes
Accepted

Merits of "Zero-Phase" Zero Padding

This is just about obtaining a symmetric signal after zero-padding. Take a symmetric signal (w.r.t. to time index $n=0$) and append zeros. Due to the implicit periodicity of the time signal used as ...
  • 80.9k
4 votes

How to Zero Pad in Order to Perform Filtering in the Fourier (Frequency) Domain?

The result of a convolution of a data vector of length M with a kernel of length G is of length M + G - 1. (the maximum length of the non-zero portion, even though the limits of integration is ...
  • 34.1k
4 votes
Accepted

Why is my time domain interpolation via zero-padding in frequency domain wrong?

The answer above is correct. Just to clarify a bit further, using x = np.linspace(0,10,5) will produce 5 numbers from 0 to 10 inclusively ...
4 votes

Relation of zero-padding and frequency resolution

why do I get "better" frequency resolution in case of adding zero-padding to this signal. You do and you don't. Zero padding increases resolution by interpolating between existing data ...
  • 33.8k
4 votes
Accepted

Why to pad zeros at the middle of sequence instead at the end of the sequence?

When working with the DFT and IFFT we can zero pad the signal, which serves to interpolate new samples in the other domain. We will often see this applied with padding at the end of the sequence or ...
  • 38.3k
3 votes
Accepted

Zeropadding and amplitude scaling

The conventional definition of the DFT for a length $N$ signal (without zero-padding) is $$X[k]=\sum_{n=0}^{N-1}x[n]e^{-j2\pi nk/N}\tag{1}$$ So there is no scaling involved. Scaling is applied to ...
  • 80.9k
3 votes

Why should I zero-pad a signal before taking the Fourier transform?

I did not see these mentioned in the prior good responses so I will add the following additional important reasons for zero padding: Radix-2 algorithms are more efficient so zero padding out to the ...
  • 38.3k
3 votes
Accepted

Relationship between z-transform and DFT

For a) you're correct. For b), $x_1$ is a length $2N$ signal, and its DFT is given by $$X_1[k]=\sum_{n=0}^{2N-1}x_1[n]e^{-j2\pi kn/2N}=\sum_{n=0}^{2N-1}x_1[n]e^{-j\pi kn/N}\tag{1}$$ With $x_1=x[n]+x[...
  • 80.9k
3 votes

How to perform a time domain shift in the frequency domain without zero padding

You must zero-pad, whether implementing the delay in the time domain or the frequency domain. (Consider this: by delaying, you are making the signal longer.) Implementing the delay with the FFT ...
  • 31
3 votes

Does Zero Padding Work as Advertised?

Zero-padding data for a longer FFT is equivalent to interpolation by a (periodic) Sinc kernel. Interpolation by a (periodic) Sinc kernel can reconstruct points between samples of a signal that was ...
  • 34.1k
3 votes

remove zero padding effect crosscorrealation

so let's say the length of your FFT is $N$. let's say that you fill half of the buffer with your signal and fill the other half with zeros. $$ x[n] = 0 \quad \text{ for } \tfrac{N}2 \le n < N $...
3 votes
Accepted

Zero padding effect on a FFT of gaussian noise

Think about both questions separately. First of all, the (I)FFT is just an implementation of the (I)DFT, so I'm going to generalize all this to the DFT. Does the zero-padded IDFT retain variance? ...
3 votes
Accepted

DFT of sum of sinusoids with random zeroed samples

The math is well known; it is the convolution theorem for the DFT. In this specific case: $$DFT\left\{f[n]\cdot z[n]\right\} = DFT\left\{f[n]\right\} * DFT\left\{z[n]\right\}$$ Where: $f[n]$ ...
  • 2,565
3 votes
Accepted

DFT zero-padding of signals starting before n=0

Use the second one Tony... It yields the correct implied phase relationship.
  • 27.1k
3 votes
Accepted

Why do the lengths of the sampled signals $x_1, \: x_2$ have to be $\text{length}(x_1)+\text{length}(x_2)-1$?

Multiplication in the frequency domain is equivalent to circular convolution in the time domain with a period of NFFT. If you don't zero pad them to at least ...
  • 2,638
3 votes
Accepted

Does Zero padding cause noise in the high frequency region?

Is that correct? No. This zero padding just leads to interpolation with a (cyclic) sinc kernel. It affects all subcarriers the same (as you can see in your own DFT!). So, this has to be a problem ...
2 votes
Accepted

FFT peak estimation: Zero-padding vs signal repetitioon

If you repeat your data, you will have discontinuities where the sequence ends meet. These will cause spurious peaks in your spectrum. You could apply a window to the data to taper it at the edges, ...
  • 2,180
2 votes

Advantages/disadvantage of zero padding

The disadvantage is you end up doing a longer FFT with higher computational cost: more MACs, energy spent toggling ALU/FPU transistors, memory paging and cache miss penalties, resulting in greater ...
  • 34.1k
2 votes

How can I increase image size by zero padding?

I suppose the array names are not descriptive of the contents and you have simply repurposed them. To zero-pad from 8x8 to 32x32: ...
2 votes

How does zero-padding affect the magnitude of the DFT?

Zero-padding does not affect DFT magnitude of the original N-DFT Samples. Overall energy does increase in the longer DFT and that is because we have introduced non-zero samples in between N-point DFT. ...
  • 2,586
2 votes
Accepted

What proportion of a padded FFT should be actual values

Be careful with this in thinking that you would increase your frequency resolution- you won't! Zero padding is very effective in iterpolating more samples between the samples you have, but it does not ...
  • 38.3k
2 votes

Spectral window when FFT is not a power of 2

500 is an exact integer multiple of the period of the cosine function used in your raised cosine window. Therefore there are zeros in the spectrum at all multiples of the cosine's frequency (due to ...
  • 34.1k

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